CN104680235A - Design method of resonance frequency of circular microstrip antenna - Google Patents

Abstract

The invention discloses a method for designing the resonant frequency of a circular microstrip antenna. The particle swarm neural network is used to determine the relationship between the three related parameters of the circular microstrip antenna patch radius, the thickness of the dielectric substrate, and the relative permittivity, and the measured resonant frequency. Establish a mapping relationship between them, use GPU technology to perform parallel acceleration calculations on the training process of the particle swarm neural network under the unified computing device architecture programming environment, and the trained particle swarm neural network can be used to predict the resonance frequency of other circular microstrip antennas . The invention can overcome the shortcoming of too long calculation time of the particle swarm neural network at the CPU end, and improve the modeling speed and modeling accuracy of the resonant frequency of the circular microstrip antenna.

Description

Design Method of Resonant Frequency of Circular Microstrip Antenna

technical field

The invention relates to a method for designing the resonant frequency of a circular microstrip antenna, in particular to a GPU-side parallel particle swarm neural network based on a unified computing device architecture, and a method for designing the resonant frequency of a circular microstrip antenna, which belongs to the technical field of antennas.

Background technique

Microstrip antennas have been widely used because of their many advantages, among which the resonant frequency is the most important parameter in the design process of microstrip antennas, which directly determines the success or failure of antenna design. Artificial Neural Networks (ANNs) models have been widely used in modeling the resonant frequency design of microstrip antennas due to their good learning and generalization capabilities. The trained neural network can establish a mapping relationship between the relevant parameters of the microstrip antenna (including patch size, dielectric substrate thickness, relative permittivity) and the measured resonance frequency, so as to complete the prediction of the resonance frequency of other microstrip antennas , this method has obvious advantages in accuracy compared with traditional methods (mainly divided into two categories: analytical method and numerical method), and can effectively overcome the shortcomings of analytical methods that are not applicable to many patch structures, and the numerical method is not suitable for patch geometric structures. The change requires a recalculation of the downside. Particle Swarm Optimization (Particle Swarm Optimization), as an easy-to-implement, fast-converging global optimization algorithm, is being gradually applied to the training of neural network weight thresholds to form the so-called Particle Swarm Optimization-Artificial Neural Networks, PSO-ANNs), can obtain better convergence accuracy and stronger prediction ability than the commonly used error backpropagation neural network, particle swarm neural network has also been used to model the resonant frequency of microstrip antennas.

A major problem in the prior art particle swarm neural network used for modeling the resonant frequency of microstrip antennas is that the training time is relatively long. The reason is that the complex network structure and the large number of particles lead to high computational complexity. Utilizing the parallelism of individual behaviors in the group that is inherent in the particle swarm optimization algorithm, using GPU technology to parallelize and accelerate the training of particle swarm neural networks is an effective way to solve this problem. Therefore, it is of great significance to study and design a GPU-side parallel particle swarm neural network based on a unified computing device architecture, which is applied to the rapid modeling of the resonant frequency of circular microstrip antennas.

Contents of the invention

The purpose of the present invention is to provide a method for designing the resonant frequency of a circular microstrip antenna. Based on the GPU-side parallel particle swarm neural network of the unified computing device architecture, the design of the resonant frequency of the circular microstrip antenna is quickly modeled to overcome the existing The shortcoming of the technical CPU-side particle swarm neural network calculation time is too long.

The purpose of the present invention is achieved through the following technical solutions:

A kind of circular microstrip antenna resonant frequency design method, comprises the following steps:

Step 1: Construct the neural network model of the resonant frequency of the circular microstrip antenna, normalize the neural network training samples and test samples of the resonant frequency of the circular microstrip antenna TM ₁₁ mode, each sample includes the patch radius, medium The four data of substrate thickness, relative permittivity and measured resonance frequency; determine the number of nodes in the input layer, hidden layer and output layer of the neural network model, and determine the activation functions of the hidden layer and output layer of the neural network model;

Step 2: Construct the particle swarm neural network model of the resonant frequency of the circular microstrip antenna, encode each particle into a D-dimensional vector X _i , where i represents the particle number, i=1, 2, ..., N, N is The number of particles in the particle swarm, the D-dimensional vector _Xi represents the ownership threshold of a neural network, and the sum of the squared errors of the normalized training samples of each neural network is the fitness value F(X _i ) of the corresponding particle. Let Determine the following parameter values in the particle swarm optimization algorithm: particle number N, inertia weight w, learning factors c ₁ and c ₂ , training times T _max ;

Step 3: Initialize the particle swarm neural network on the CPU side: randomly initialize the position X _id and velocity V _id of each particle, d=1, 2, ..., D, and calculate the fitness value F(X _i ) of each particle , the initial value of the individual optimal fitness value F(P _{i, best} ) of each particle is set to F(X _i ), the individual optimal position P _{id of each particle, the initial value of best} is set to X _id , all F( The minimum value of P _{i, best} and its corresponding position are respectively set as the global optimal fitness value F (G _best ) and the global optimal position G _{d, best} ;

Step 4: Transfer data from the CPU end to the GPU end: the CPU end calls the cudaMemcpy() function to transfer the CPU end data X _id , V _id , F(X _i ), P _{id, best} , F(P _{i, best} ), G _{d, best} and F(G _best ) are transferred to the GPU global memory; the CPU side calls the cudaMemcpyToSymbol() function to transfer the normalized training sample data from the CPU side to the GPU constant memory;

Step 5: Perform parallel particle swarm neural network calculation on the GPU side: using the parallelism of individual behaviors in the PSO algorithm group, one thread on the GPU side corresponds to one particle, and repeatedly execute T _max parallel particle swarm neural network algorithm iterations on the GPU side, each time The parallel particle swarm neural network algorithm includes the following four steps (1)(2)(3)(4) executed sequentially:

(1) Simultaneously update the velocity V _id (t) and position X _id (t) of each particle according to the particle swarm velocity update and position update formulas:

V _id (t+1)＝wV _id (t)+c ₁ r ₁ (P _id，best (t)-X _id (t))+c ₂ r ₂ (G _d，best (t)-X _id ( t))

X _id (t+1)＝X _id (t)+V _id (t+1)

In the formula, the current number of iterations t=1, 2, ..., T _max , r ₁ and r ₂ are uniformly distributed random numbers between [0, 1]. To generate random numbers on the GPU side, you can use the CURAND library curand_uniform() function);

(2) Simultaneously calculate the fitness value F(X _i ) corresponding to each particle;

(3) Simultaneously update the individual optimal fitness value F(P _{i, best} ) of each particle and its corresponding individual optimal position P _{id, best} : if F(X _i )<F(P _{i, best} ), Then F(X _i )=F(P _{i, best} ), P _{id, best} =X _id ;

(4) Use the parallel reduction algorithm to update the global optimal fitness value F(G _best ) and its corresponding global optimal position G _{d, best} : if min(F(P _{i, best} ))<F(G _best ), Then F(G _best )=min(F(P _{i, best} )), i=I when getting min, G _{d, best} =P _{Id, best} ;

Step 6: Perform data transfer from the GPU end to the CPU end, that is, the CPU end calls the cudaMemcpy() function, and the optimal weight threshold G _{d, best of} the neural network trained on the GPU end is sent back to the CPU end;

Step 7: Bring the normalized training samples and test samples into the trained neural network, and reverse the network output to obtain the network output value of the resonant frequency of the circular microstrip antenna.

The object of the present invention can also be further realized by the following technical measures:

Aforesaid circular microstrip antenna resonant frequency design method, wherein the number of nodes of the input layer, hidden layer and output layer of neural network described in step 1 is:

The neural network adopts a commonly used 3-layer network structure. The number i of network input layer nodes is 3, the number j of output layer nodes is 1, and the value range of the hidden layer node number p is determined by the following formula:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; ;</span>$

Wherein the activation function of the hidden layer and the output layer of the neural network described in step 1 is determined as follows:

The activation function of the hidden layer of the neural network is selected as a bipolar S-type function, as shown in the following formula:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; ;</span>$

The activation function of the output layer is selected as a unipolar S-type function, as shown in the following formula:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; .</span>$

In the method for designing the resonant frequency of the circular microstrip antenna, the number p of hidden layer nodes in step 1 is set to 8.

The method for designing the resonant frequency of the aforementioned circular microstrip antenna, wherein the particle dimension D of the vector X _i in step 2 is 41.

The method for designing the resonant frequency of the aforementioned circular microstrip antenna, wherein the number of particles N described in step 2 is a multiple of 64; the value of the inertia weight w is 1 to 0.4 linearly decreasing; the learning factors _c1 and _c2 are respectively 2.8 and 1.3; The training times T _max is set to 1000.

Compared with prior art, the beneficial effect of the present invention is:

(1) The parallel acceleration training of the particle swarm neural network is realized by processing the calculation process of each particle in parallel on the GPU side, which significantly reduces the modeling time of the resonant frequency of the circular microstrip antenna. Can obtain 347 times of calculation acceleration ratio; (2) the more the number of particles, the higher the acceleration ratio obtained; (3) the present invention greatly increases the number of particles is a special method to adapt to the GPU computing architecture; with the increase of the number of particles, and Compared with the serial particle swarm neural network on the CPU side of the prior art, the running time of the parallel particle swarm neural network on the GPU side is extremely limited; if the number of particles is greatly increased on the GPU side, this method can achieve a very limited increase in modeling time. The modeling error is greatly reduced, and the modeling error performance is better than that of all existing technologies.

Description of drawings

Fig. 1 is a circular microstrip antenna model diagram;

Fig. 2 is a diagram of a programming model of a unified computing device architecture;

Fig. 3 is the flow chart of circular microstrip antenna resonant frequency design method of the present invention;

Fig. 4 is the neural network training sample and test sample of the resonant frequency under the circular microstrip antenna TM ₁₁ mode;

Fig. 5 is the particle swarm vector coding model of 3-8-1 structure neural network;

6 is a configuration diagram of a computing device platform used in the present invention;

Figure 7 shows the calculation acceleration ratio data obtained by modeling the resonant frequency of the circular microstrip antenna TM ₁₁ mode by the parallel particle swarm neural network on the GPU side;

Figure 8 shows the average absolute error sum data between the network output value and the measured value of the resonant frequency of the circular microstrip antenna TM ₁₁ mode obtained by various CPU-side neural network models in the existing literature.

Detailed ways

Aiming at the problem that the calculation time is too long when the particle swarm neural network models the resonant frequency of the circular microstrip antenna, the present invention designs and implements a unified computing device architecture based on the existing GPU-side parallel particle swarm algorithm research. The GPU-side parallel particle swarm neural network solution method is used, and the resonant frequency of the circular microstrip antenna is quickly modeled, which improves the modeling speed and modeling accuracy.

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Fig. 1 is a circular microstrip antenna model, the radius of the circular patch 1 is a, the thickness of the dielectric substrate 2 is h, and the relative permittivity is ε _r . The cavity model method is used to analyze the circular patch. When h<<λ ₀ , the cavity between the patch 1 and the ground plate 3 can be regarded as a thin cylindrical resonant space with magnetic walls around and electric walls up and down. cavity, the electric field in the cavity should be a transverse magnetic wave (Transverse-magnetic Wave, TM wave) mode with only E _z component. Expand E _z as a superposition of eigenfunctions:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}{\mathrm{<span\; class="notranslate">\; \&Psi;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The eigenfunctions and boundary conditions should have the following form:

J _m ′(k _mn a)＝0 (5) In the formula, J _m (k _mn ρ) is an m-order Bessel function, k _mn is a separation parameter, and

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the formula, χ′ _mn is the nth root of the function J _m ′(χ). The resonant frequency of the circular microstrip antenna can be approximated by k=k _mn

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; c\&chi;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;a</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, c is the propagation speed of electromagnetic wave in free space, and m and n are integers. When calculating the resonant frequency of the main mode TM ₁₁ mode of the circular patch, equation (7) can be written as

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.293</span>}\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

If the edge effect is considered, the radius a in the formula can be replaced by the equivalent radius a _e calculated by the following empirical formula:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;a\&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; \&pi;a</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1.7726</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Obviously, the resonant frequency of circular microstrip antenna depends on a, h, ε _r , m, n; in TM ₁₁ mode, it depends on a, h, ε _r .

As shown in Figure 2, the unified computing device architecture programming model takes the CPU as the host and the GPU as the coprocessor, and the two work together to perform their duties. The CPU is responsible for logical transaction processing and serial computing, while the GPU focuses on executing highly threaded parallel processing tasks. The unified computing device architecture adopts the Single Instruction Multiple Threads (Single Instruction MultipleThreads, SIMT) execution mode. The kernel function performs parallel computing tasks on the GPU, and is a step in the entire program that can be executed in parallel. The unified computing device architecture organizes threads into three different levels: Grid, Block, and Thread, and adopts a multi-level memory structure: local memory that is only visible to a single thread, and Shared memory visible to threads within a block, global memory visible to all threads, etc. There are two levels of parallelism in a kernel function, that is, coarse-grained parallelism that does not require communication between thread blocks in the same grid, and fine-grained parallelism that allows communication between threads in the same thread block. The computing process of the unified computing device architecture usually includes three steps: CPU-to-GPU data transfer, kernel function execution, and GPU-to-CPU data transfer.

As shown in Figure 3, the algorithm flow chart of the rapid modeling of the resonant frequency design of the circular microstrip antenna TM ₁₁ mode based on the GPU-side parallel particle swarm neural network based on the unified computing device architecture, the specific steps are as follows:

Step 1: Construct the neural network model of the resonant frequency of the circular microstrip antenna, including the neural network training samples and test samples of the resonant frequency of the circular microstrip antenna TM ₁₁ mode (each sample includes patch radius, dielectric substrate thickness , relative permittivity and measured resonance frequency) normalized processing, determine the number of nodes in the input layer, hidden layer and output layer of the neural network, and determine the activation function of the hidden layer and output layer of the neural network.

(1) The neural network training samples and test samples of the resonant frequency in the circular microstrip antenna TM ₁₁ mode (each sample contains four data of patch radius, dielectric substrate thickness, relative permittivity and measured resonant frequency) Normalization processing.

Figure 4 lists 16 sets of training samples (without asterisks) and 4 sets of test samples (with asterisks), among which the patch radius, dielectric substrate thickness, and relative permittivity of the circular microstrip antenna are three The relevant parameters (a, h, ε _r ) are taken as network input (columns 2 to 4 in Fig. 4), and the corresponding measured resonant frequency f _ME in TM ₁₁ mode is taken as network output (column 5 in Fig. 4). For the convenience of data processing, each column of data is normalized, and the data range is limited to [0, 1]. Normalized training samples are used for neural network training.

(2) Determine the number of nodes in the input layer, hidden layer and output layer of the neural network.

The neural network adopts a commonly used 3-layer network structure. The number i of network input layer nodes is 3 (corresponding to a, h, ε _r respectively), the number j of output layer nodes is 1 (corresponding to the resonance frequency), and the value of the hidden layer node number p is The range is determined by the following formula:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Preferably, the number p of hidden layer nodes is set to 8, so that the neural network structure is 3-8-1.

(3) Determine the activation function of the hidden layer and output layer of the neural network.

According to the characteristics of the problem, the activation function of the hidden layer of the neural network is selected as a bipolar S-type function, and its expression is shown in formula (11); the activation function of the output layer is selected as a unipolar S-type function, and its expression is as follows (12).

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Step 2: Construct the particle swarm neural network model of the resonant frequency of the circular microstrip antenna, including encoding each particle into a D-dimensional vector X _i (i represents the particle number, i=1, 2, ..., N, N is the number of particles in the particle swarm) represents the ownership threshold of a neural network, and the sum of squared error (Sum of Squared Error, SSE) output of each neural network’s normalized training samples is the fitness value F(X _i ); set the following parameter values in the particle swarm optimization algorithm: particle number N, inertia weight w, learning factors c ₁ and c ₂ , training times T _max .

(1) encode each particle into a D-dimensional vector _Xi (i represents the particle number, i=1, 2, ..., N, N is the number of particles in the particle swarm) represents the ownership threshold of a neural network, The output sum of squared error (Sum of Squared Error, SSE) of the normalized training samples of each neural network is the fitness value F(X _i ) of the corresponding particle.

Fig. 5 is the particle swarm vector coding model of the 3-8-1 structure neural network. This model adopts the principle of one-to-one correspondence between each dimension of the particle and each weight threshold of the neural network, and encodes each particle into a particle dimension (problem dimension , weight threshold number) D is 41 vector _Xi (i represents the particle number, i=1, 2, ..., N, N is the number of particles in the particle swarm) represents the ownership threshold of a neural network, such as formula ( 13); the sum of squared error (Sum of SquaredError, SSE) output of the normalized training samples of each neural network is the fitness value F(X _i ) of the corresponding particle.

X _i ＝[X _i1 X _i2 X _i3 ... X _i39 X _i40 X _i41 ] (13)

(2) Set the following parameter values in the particle swarm optimization algorithm: particle number N, inertia weight w, learning factors c ₁ and c ₂ , training times T _max .

In the unified computing device architecture, a thread warp (Warp) contains 32 threads adjacent to each other, and the stream multiprocessor (StreamMultiprocessor, SM) schedules and executes threads in units of thread warps, so the number of particles N is designed to be a multiple of 32 , and because the number of particles is generally greater than the problem dimension of 41, the number of particles N is designed to be a multiple of 64; the inertia weight w is linearly decreased from 1 to 0.4; the learning factors c ₁ and c ₂ are 2.8 and 1.3 respectively; The number of training times T _max is 1000.

Step 3: Initialize the particle swarm neural network on the CPU side, including randomly initializing the position X _id and velocity V _id (d=1, 2, ..., D) of each particle, and calculating the fitness value F(X _i ), the initial value of the individual optimal fitness value F(P _{i, best} ) of each particle is set to F(X _i ), the individual optimal position P _{id of each particle, the initial value of best} is set to X _id , all The minimum value of F(P _{i, best} ) and its corresponding position are respectively set as the global optimal fitness value F(G _best ) and the global optimal position G _{d, best} .

Step 4: Data transfer from the CPU end to the GPU end, including calling the cudaMemcpy() function on the CPU end to transfer the particle data X _id , V _id , F(X _i ), P _{id, best} , F(P _{i, best} ), G _{d, best} , F(G _best ) are transferred to the GPU global memory; the CPU side calls the cudaMemcpyToSymbol() function to transfer the normalized training sample data from the CPU side to the GPU constant memory.

Step 5: Parallel particle swarm neural network calculation on the GPU side, including using the parallelism of individual behaviors in the PSO algorithm group, one thread on the GPU side corresponds to one particle, and repeatedly execute T _max times of parallel particle swarm neural network algorithm iterations on the GPU side, each time The parallel particle swarm neural network algorithm includes the following four steps (1)(2)(3)(4) executed sequentially:

(1) Simultaneously update the velocity V _id (t) and position X _id (t) of each particle according to the particle swarm velocity update and position update formulas;

V _id (t+1)＝wV _id (t)+c ₁ r ₁ (P _id，best (t)-X _id (t))+c ₂ r ₂ (G _d，best (t)-X _id ( t)) (1)

X _id (t+1)＝X _id (t)+V _id (t+1) (2)

In the formula, the current number of iterations t=1, 2, ..., T _max , r ₁ and r ₂ are uniformly distributed random numbers between [0, 1] (random numbers generated on the GPU side can be used in the CURAND library curand_uniform() function);

(2) Simultaneously calculate the fitness value F(X _i ) corresponding to each particle;

(3) Simultaneously update the individual optimal fitness value F(P _{i, best} ) of each particle and its corresponding individual optimal position P _{id, best} : if F(X _i )<F(P _{i, best} ), Then F(X _i )=F(P _{i, best} ), P _{id, best} =X _id ;

(4) Use the parallel reduction algorithm to update the global optimal fitness value F(G _best ) and its corresponding global optimal position G _{d, best} : if min(F(P _{i, best} ))<F(G _best ), Then F(G _best )=min(F(P _i,best )) (i=I when taking min), G _d,best =P _Id,best .

Step 6: Data transfer from the GPU end to the CPU end, including calling the cudaMemcpy() function on the CPU end, and transferring the optimal weight threshold G _{d, best} of the neural network trained on the GPU end to the CPU end.

Step 7: Bring the normalized training samples and test samples into the trained neural network, and reverse the network output to obtain the network output value of the resonant frequency of the circular microstrip antenna. Calculate the sum of the absolute errors between the network output value and the measured value, record the total running time of the program, and perform performance analysis on the modeling speed and modeling error.

According to the above steps, the numerical test is carried out under the equipment environment shown in Figure 6, and the results are shown in Figure 7. The "computing acceleration ratio" item in Figure 7 is used as a commonly used acceleration performance index, which is defined as the running time of the CPU-side program and the GPU-side program running time of the particle swarm neural network under the same number of particles and the same number of iterations (1000 times in the experiment). ratio. Fig. 8 has listed the average absolute error summation between the network output value of resonant frequency and measured value under the circular microstrip antenna TM ₁₁ mode that various CPU end neural network models obtain in the existing literature, to facilitate calculation with the present invention The results are compared.

Analyze Figures 7 and 8 as follows:

(a) The larger the number of particles, the higher the computing speedup ratio obtained, and the GPU-side parallel particle swarm neural network achieved a speedup ratio of up to 347 times. With the doubling of the number of particles, when the number of particles is less than or equal to 16384 (the maximum number of resident threads of the GPU used is 26624), the calculation speedup ratio is roughly doubled; when the number of particles is greater than or equal to 32768, the calculation speedup ratio can still be increased but the speedup is slowed down. slow.

(b) The GPU-side parallel particle swarm neural network has the same optimization stability as the CPU-side serial particle swarm neural network. As the number of particles continues to increase, the errors of the CPU program and the GPU program continue to decrease; when the number of particles is the same, the errors of the CPU program and the GPU program are roughly the same or similar.

(c) Substantially increasing the number of particles is a special way to adapt to the GPU computing architecture. As the number of particles increases, there is a very limited increase in runtime on the GPU side compared to the CPU side. The modeling error of the GPU-side parallel particle swarm neural network is better than the result of BP in the literature when the number of particles is greater than or equal to 256; when the number of particles is greater than or equal to 1024, it is better than the result of DBD in the literature; when the number of particles is greater than or equal to 8192 When the number of particles is greater than or equal to 32768, it is better than the results of EDBD in the literature; when the number of particles is greater than or equal to 65536, it is better than the results of all existing literatures including BiPSO in the literature.

The above analysis is summarized as follows:

(1) If the GPU side uses the same number of particles as the CPU side, this method can greatly reduce the modeling time under the premise of convergence consistency.

(2) If the number of particles is greatly increased on the GPU side, this method can greatly reduce the modeling error with a very limited increase in modeling time.

The method can greatly reduce the modeling error with a very limited increase in modeling time, and the modeling error performance is better than that of all existing technologies.

In addition to the above-mentioned embodiments, the present invention can also have other implementations, and all technical solutions formed by equivalent replacement or equivalent transformation fall within the scope of protection required by the present invention.

Claims (5)

1. a circular microstrip antenna resonant frequency design method, is characterized in that, the method comprises the following steps; Step 1: Construct the neural network model of the resonant frequency of the circular microstrip antenna, normalize the neural network training samples and test samples of the resonant frequency of the circular microstrip antenna TM ₁₁ mode, each sample includes the patch radius, medium The four data of substrate thickness, relative permittivity and measured resonance frequency; determine the number of nodes in the input layer, hidden layer and output layer of the neural network model, and determine the activation functions of the hidden layer and output layer of the neural network model; Step 2: Construct the particle swarm neural network model of the resonant frequency of the circular microstrip antenna, encode each particle into a D-dimensional vector X _i , where i represents the particle number, i=1,2,...,N, where N is The number of particles in the particle swarm, the D-dimensional vector _Xi represents the ownership threshold of a neural network, and the sum of the squared errors of the normalized training samples of each neural network is the fitness value F(X _i ) of the corresponding particle. Let Determine the following parameter values in the particle swarm optimization algorithm: particle number N, inertia weight w, learning factors c ₁ and c ₂ , training times T _max ; Step 3: Initialize the particle swarm neural network on the CPU side; randomly initialize the position X _id and velocity V _id of each particle, d=1,2,...,D, and calculate the fitness value F(X _i ) of each particle , the initial value of the individual optimal fitness value F(P _i,best ) of each particle is set to F(X _i ), the initial value of the individual optimal position P _{id,best of} each particle is set to X _id , all F( The minimum value of P _i,best ) and its corresponding position are respectively set as the global optimal fitness value F(G _best ) and the global optimal position G _d,best ; Step 4: Transfer data from the CPU end to the GPU end: the CPU end calls the cudaMemcpy() function to transfer the CPU end data X _id , V _id , F(X _i ), P _id,best , F(P _i,best ), G _{d, best} and F(G _best ) are transferred to the GPU global memory; the CPU side calls the cudaMemcpyToSymbol() function to transfer the normalized training sample data from the CPU side to the GPU constant memory; Step 5: Perform parallel particle swarm neural network calculation on the GPU side: using the parallelism of individual behaviors in the PSO algorithm group, one thread on the GPU side corresponds to one particle, and repeatedly execute T _max parallel particle swarm neural network algorithm iterations on the GPU side, each time The parallel particle swarm neural network algorithm includes the following four steps (1)(2)(3)(4) executed sequentially: (1) Simultaneously update the velocity V _id (t) and position X _id (t) of each particle according to the particle swarm velocity update and position update formulas: V _id (t+1)＝wV _id (t)+c ₁ r ₁ (P _id,best (t)-X _id (t))+c ₂ r ₂ (G _d,best (t)–X _id ( t)) X _id (t+1)＝X _id (t)+V _id (t+1) In the formula, the current number of iterations t=1,2,...,T _max , r ₁ and r ₂ are uniformly distributed random numbers between [0,1]. To generate random numbers on the GPU side, you can use the CURAND library curand_uniform() function); (2) Simultaneously calculate the fitness value F(X _i ) corresponding to each particle; (3) Simultaneously update the individual optimal fitness value F(P _i,best ) of each particle and its corresponding individual optimal position P _id,best ; if F(X _i )<F(P _i,best ), Then F(X _i )=F(P _i,best ), P _id,best =X _id ; (4) Use the parallel reduction algorithm to update the global optimal fitness value F(G _best ) and its corresponding global optimal position G _d,best : if min(F(P _i,best ))<F(G _best ), Then F(G _best )=min(F(P _{i, best} )), i=I when getting min, G _{d, best} =P _{Id, best} ; Step 6: Perform data transfer from the GPU end to the CPU end, that is, the CPU end calls the cudaMemcpy() function to transfer the optimal weight threshold G _d,best of the neural network trained on the GPU end to the CPU end; Step 7: Bring the normalized training samples and test samples into the trained neural network, and reverse the network output to obtain the network output value of the resonant frequency of the circular microstrip antenna. 2. circular microstrip antenna resonance frequency design method as claimed in claim 1, is characterized in that, the number of nodes of the input layer of neural network described in step 1, hidden layer and output layer is: The neural network adopts a commonly used 3-layer network structure. The number i of network input layer nodes is 3, the number j of output layer nodes is 1, and the value range of the hidden layer node number p is determined by the following formula: $\begin{array}{cc}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 10</span>}\end{array}<span\; class="notranslate">\; ;</span>$ The activation functions of the hidden layer and the output layer of the neural network described in step 1 are determined as follows: The activation function of the hidden layer of the neural network is selected as a bipolar S-type function, as shown in the following formula; $\begin{array}{cc}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>\end{array}<span\; class="notranslate">\; ;</span>$ The activation function of the output layer is selected as a unipolar S-type function, as shown in the following formula; $\begin{array}{cc}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}& <span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>\end{array}<span\; class="notranslate">\; .</span>$ 3. the circular microstrip antenna resonant frequency design method as claimed in claim 2, is characterized in that, described hidden layer node number p is set to 8. 4. the circular microstrip antenna resonant frequency design method as claimed in claim 3, is characterized in that, the particle dimension D of vector _Xi described in step 2 is 41. 5. circular microstrip antenna resonant frequency design method as claimed in claim 4, is characterized in that, the multiple value of particle number N described in step 2 is 64; Inertia weight w takes a value of 1 to 0.4 linear decline; Learning factor c ₁ and c ₂ are set to 2.8 and 1.3 respectively; the number of training T _max is set to 1000.